Borel-Écalle resummation of a two-point function
- We provide an overview of the tools and techniques of resurgence theory used in the Borel-ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-ecalle summable.
| Author details: | Pierre J. ClavierGND |
|---|---|
| DOI: | https://doi.org/10.1007/s00023-021-01057-w |
| ISSN: | 1424-0637 |
| ISSN: | 1424-0661 |
| Title of parent work (English): | Annales Henri Poincaré : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincaré and by the Swiss Physical Society |
| Publisher: | Springer |
| Place of publishing: | Cham |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/04/26 |
| Publication year: | 2021 |
| Release date: | 2023/09/27 |
| Volume: | 22 |
| Issue: | 6 |
| Number of pages: | 34 |
| First page: | 2103 |
| Last Page: | 2136 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
| Peer review: | Referiert |
